Let f be a multiplier for the Drury-Arveson space H n of the unit ball, and let ζ1, ..., ζn denote the coordinate functions. We show that for each 1 ≤ i ≤ n, the commutator [M∗ f ,Mζi ] belongs to the Schatten class Cp, p > 2n. This leads to a localization result for multipliers.

We investigate the Weyl calculus of pseudodifferential operators with the methods of time-frequency analysis. As symbol classes we use the modulation spaces, which are the function spaces associated to the short-time Fourier transform and the Wigner distribution. We investigate the boundedness and Schatten-class properties of pseudodifferential operators, and furthermore we study their mapping ...

We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten operators is simultaneously triangularizable.

The paper contains three results, the common feature of which is that they deal with the Schatten p class. The first is a presentation of a new complemented subspace of Cp in the reflexive range (and p ̸= 2). This construction answers a question of Arazy and Lindestrauss from 1975. The second result relates to tight embeddings of finite dimensional subspaces of Cp in C n p with small n and shows...

We study when multiplication by a weight can turn non-compact composition operator on \(H^2\) into compact operator, and it be in Schatten classes. The \(q\)-summing case \(H^p\) is considered. also this one.

We study Cwikel-type estimates for the singular values and Schatten Lp-norms of compositions multiplication convolution operators acting on stratified Lie groups. This enables us to obtain novel spectral asymptotic formulas certain derived from sub-Laplacians.